SOLUTION: In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

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Question 87271: In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=# of votes for winning candidate, L=# of votes for losing candidate

Since the total of votes cast was 810 (ie the sum of both candidates votes), we get the equation

w%2BL=810

Since the winning candidate had 220 more votes than the losing candidate, this means that we simply add 220 to L to find w like this

w=220%2BL

For instance, lets say the losing candidate had 2 votes, then the winning candidate would have 220%2B2=222 votes

Since w=220%2BL, we can replace the w of the equation w%2BL=810

highlight%28220%2BL%29%2BL=810 Plug in w=220%2BL

220%2B2L=810 Combine like terms

cross%28220-220%29%2B2L=810-220 Subtract 220 from both sides

2L=590 Combine like terms on the right side

L=590%2F2 Divide both sides by 2

So we get
L=295
This means the losing candidate had 295 votes. To find out how many the winning candidate received, lets plug in L=295 into the other equation:

w%2Bhighlight%28295%29=810 Plug in L=295

w%2Bcross%28295-295%29=810-295 Subtract 295 from both sides

w=515

So the winning candidate received 515 votes and the losing received had 295 votes.

Check:
515%2B295=810 Plug in w=515 and L=295

810=810 works